import torch import torch.nn as nn import torch.nn.functional as F import math import numpy as np import numpy as np import math from math import sqrt class PositionalEmbedding(nn.Module): def __init__(self, d_model, max_len=5000): super(PositionalEmbedding, self).__init__() # Compute the positional encodings once in log space. pe = torch.zeros(max_len, d_model).float() pe.require_grad = False position = torch.arange(0, max_len).float().unsqueeze(1) div_term = (torch.arange(0, d_model, 2).float() * -(math.log(10000.0) / d_model)).exp() pe[:, 0::2] = torch.sin(position * div_term) pe[:, 1::2] = torch.cos(position * div_term) pe = pe.unsqueeze(0) self.register_buffer('pe', pe) def forward(self, x): return self.pe[:, :x.size(1)] class TokenEmbedding(nn.Module): def __init__(self, c_in, d_model): super(TokenEmbedding, self).__init__() padding = 1 if torch.__version__ >= '1.5.0' else 2 self.tokenConv = nn.Conv1d(in_channels=c_in, out_channels=d_model, kernel_size=3, padding=padding, padding_mode='circular', bias=False) for m in self.modules(): if isinstance(m, nn.Conv1d): nn.init.kaiming_normal_( m.weight, mode='fan_in', nonlinearity='leaky_relu') def forward(self, x): x = self.tokenConv(x.permute(0, 2, 1)).transpose(1, 2) return x class FixedEmbedding(nn.Module): def __init__(self, c_in, d_model): super(FixedEmbedding, self).__init__() w = torch.zeros(c_in, d_model).float() w.require_grad = False position = torch.arange(0, c_in).float().unsqueeze(1) div_term = (torch.arange(0, d_model, 2).float() * -(math.log(10000.0) / d_model)).exp() w[:, 0::2] = torch.sin(position * div_term) w[:, 1::2] = torch.cos(position * div_term) self.emb = nn.Embedding(c_in, d_model) self.emb.weight = nn.Parameter(w, requires_grad=False) def forward(self, x): return self.emb(x).detach() class TemporalEmbedding(nn.Module): def __init__(self, d_model, embed_type='fixed', freq='h'): super(TemporalEmbedding, self).__init__() minute_size = 4 hour_size = 24 weekday_size = 7 day_size = 32 month_size = 13 Embed = FixedEmbedding if embed_type == 'fixed' else nn.Embedding if freq == 't': self.minute_embed = Embed(minute_size, d_model) self.hour_embed = Embed(hour_size, d_model) self.weekday_embed = Embed(weekday_size, d_model) self.day_embed = Embed(day_size, d_model) self.month_embed = Embed(month_size, d_model) def forward(self, x): x = x.long() minute_x = self.minute_embed(x[:, :, 4]) if hasattr( self, 'minute_embed') else 0. hour_x = self.hour_embed(x[:, :, 3]) weekday_x = self.weekday_embed(x[:, :, 2]) day_x = self.day_embed(x[:, :, 1]) month_x = self.month_embed(x[:, :, 0]) return hour_x + weekday_x + day_x + month_x + minute_x class TimeFeatureEmbedding(nn.Module): def __init__(self, d_model, embed_type='timeF', freq='h'): super(TimeFeatureEmbedding, self).__init__() freq_map = {'h': 4, 't': 5, 's': 6, 'm': 1, 'a': 1, 'w': 2, 'd': 3, 'b': 3} d_inp = freq_map[freq] self.embed = nn.Linear(d_inp, d_model, bias=False) def forward(self, x): return self.embed(x) class DataEmbedding(nn.Module): def __init__(self, c_in, d_model, embed_type='fixed', freq='h', dropout=0.1): super(DataEmbedding, self).__init__() self.value_embedding = TokenEmbedding(c_in=c_in, d_model=d_model) self.position_embedding = PositionalEmbedding(d_model=d_model) self.temporal_embedding = TemporalEmbedding(d_model=d_model, embed_type=embed_type, freq=freq) if embed_type != 'timeF' else TimeFeatureEmbedding( d_model=d_model, embed_type=embed_type, freq=freq) self.dropout = nn.Dropout(p=dropout) def forward(self, x, x_mark): if x_mark is None: x = self.value_embedding(x) + self.position_embedding(x) else: x = self.value_embedding( x) + self.temporal_embedding(x_mark) + self.position_embedding(x) return self.dropout(x) class DataEmbedding_inverted(nn.Module): def __init__(self, c_in, d_model, embed_type='fixed', freq='h', dropout=0.1): super(DataEmbedding_inverted, self).__init__() self.value_embedding = nn.Linear(c_in, d_model) self.dropout = nn.Dropout(p=dropout) def forward(self, x, x_mark): x = x.permute(0, 2, 1) # x: [Batch Variate Time] if x_mark is None: x = self.value_embedding(x) else: x = self.value_embedding(torch.cat([x, x_mark.permute(0, 2, 1)], 1)) # x: [Batch Variate d_model] return self.dropout(x) class DataEmbedding_wo_pos(nn.Module): def __init__(self, c_in, d_model, embed_type='fixed', freq='h', dropout=0.1): super(DataEmbedding_wo_pos, self).__init__() self.value_embedding = TokenEmbedding(c_in=c_in, d_model=d_model) self.position_embedding = PositionalEmbedding(d_model=d_model) self.temporal_embedding = TemporalEmbedding(d_model=d_model, embed_type=embed_type, freq=freq) if embed_type != 'timeF' else TimeFeatureEmbedding( d_model=d_model, embed_type=embed_type, freq=freq) self.dropout = nn.Dropout(p=dropout) def forward(self, x, x_mark): if x_mark is None: x = self.value_embedding(x) else: x = self.value_embedding(x) + self.temporal_embedding(x_mark) return self.dropout(x) class PatchEmbedding(nn.Module): def __init__(self, d_model, patch_len, stride, padding, dropout): super(PatchEmbedding, self).__init__() # Patching self.patch_len = patch_len self.stride = stride self.padding_patch_layer = nn.ReplicationPad1d((0, padding)) # Backbone, Input encoding: projection of feature vectors onto a d-dim vector space self.value_embedding = nn.Linear(patch_len, d_model, bias=False) # Positional embedding self.position_embedding = PositionalEmbedding(d_model) # Residual dropout self.dropout = nn.Dropout(dropout) def forward(self, x): # do patching n_vars = x.shape[1] x = self.padding_patch_layer(x) x = x.unfold(dimension=-1, size=self.patch_len, step=self.stride) x = torch.reshape(x, (x.shape[0] * x.shape[1], x.shape[2], x.shape[3])) # Input encoding x = self.value_embedding(x) + self.position_embedding(x) return self.dropout(x), n_vars class AutoCorrelation(nn.Module): """ AutoCorrelation Mechanism with the following two phases: (1) period-based dependencies discovery (2) time delay aggregation This block can replace the self-attention family mechanism seamlessly. """ def __init__(self, mask_flag=True, factor=1, scale=None, attention_dropout=0.1, output_attention=False): super(AutoCorrelation, self).__init__() self.factor = factor self.scale = scale self.mask_flag = mask_flag self.output_attention = output_attention self.dropout = nn.Dropout(attention_dropout) def time_delay_agg_training(self, values, corr): """ SpeedUp version of Autocorrelation (a batch-normalization style design) This is for the training phase. """ head = values.shape[1] channel = values.shape[2] length = values.shape[3] # find top k top_k = int(self.factor * math.log(length)) mean_value = torch.mean(torch.mean(corr, dim=1), dim=1) index = torch.topk(torch.mean(mean_value, dim=0), top_k, dim=-1)[1] weights = torch.stack([mean_value[:, index[i]] for i in range(top_k)], dim=-1) # update corr tmp_corr = torch.softmax(weights, dim=-1) # aggregation tmp_values = values delays_agg = torch.zeros_like(values).float() for i in range(top_k): pattern = torch.roll(tmp_values, -int(index[i]), -1) delays_agg = delays_agg + pattern * \ (tmp_corr[:, i].unsqueeze(1).unsqueeze(1).unsqueeze(1).repeat(1, head, channel, length)) return delays_agg def time_delay_agg_inference(self, values, corr): """ SpeedUp version of Autocorrelation (a batch-normalization style design) This is for the inference phase. """ batch = values.shape[0] head = values.shape[1] channel = values.shape[2] length = values.shape[3] # index init init_index = torch.arange(length).unsqueeze(0).unsqueeze(0).unsqueeze(0).repeat(batch, head, channel, 1).to(values.device) # find top k top_k = int(self.factor * math.log(length)) mean_value = torch.mean(torch.mean(corr, dim=1), dim=1) weights, delay = torch.topk(mean_value, top_k, dim=-1) # update corr tmp_corr = torch.softmax(weights, dim=-1) # aggregation tmp_values = values.repeat(1, 1, 1, 2) delays_agg = torch.zeros_like(values).float() for i in range(top_k): tmp_delay = init_index + delay[:, i].unsqueeze(1).unsqueeze(1).unsqueeze(1).repeat(1, head, channel, length) pattern = torch.gather(tmp_values, dim=-1, index=tmp_delay) delays_agg = delays_agg + pattern * \ (tmp_corr[:, i].unsqueeze(1).unsqueeze(1).unsqueeze(1).repeat(1, head, channel, length)) return delays_agg def time_delay_agg_full(self, values, corr): """ Standard version of Autocorrelation """ batch = values.shape[0] head = values.shape[1] channel = values.shape[2] length = values.shape[3] # index init init_index = torch.arange(length).unsqueeze(0).unsqueeze(0).unsqueeze(0).repeat(batch, head, channel, 1).to(values.device) # find top k top_k = int(self.factor * math.log(length)) weights, delay = torch.topk(corr, top_k, dim=-1) # update corr tmp_corr = torch.softmax(weights, dim=-1) # aggregation tmp_values = values.repeat(1, 1, 1, 2) delays_agg = torch.zeros_like(values).float() for i in range(top_k): tmp_delay = init_index + delay[..., i].unsqueeze(-1) pattern = torch.gather(tmp_values, dim=-1, index=tmp_delay) delays_agg = delays_agg + pattern * (tmp_corr[..., i].unsqueeze(-1)) return delays_agg def forward(self, queries, keys, values, attn_mask): B, L, H, E = queries.shape _, S, _, D = values.shape if L > S: zeros = torch.zeros_like(queries[:, :(L - S), :]).float() values = torch.cat([values, zeros], dim=1) keys = torch.cat([keys, zeros], dim=1) else: values = values[:, :L, :, :] keys = keys[:, :L, :, :] # period-based dependencies q_fft = torch.fft.rfft(queries.permute(0, 2, 3, 1).contiguous(), dim=-1) k_fft = torch.fft.rfft(keys.permute(0, 2, 3, 1).contiguous(), dim=-1) res = q_fft * torch.conj(k_fft) corr = torch.fft.irfft(res, dim=-1) # time delay agg if self.training: V = self.time_delay_agg_training(values.permute(0, 2, 3, 1).contiguous(), corr).permute(0, 3, 1, 2) else: V = self.time_delay_agg_inference(values.permute(0, 2, 3, 1).contiguous(), corr).permute(0, 3, 1, 2) if self.output_attention: return (V.contiguous(), corr.permute(0, 3, 1, 2)) else: return (V.contiguous(), None) class AutoCorrelationLayer(nn.Module): def __init__(self, correlation, d_model, n_heads, d_keys=None, d_values=None): super(AutoCorrelationLayer, self).__init__() d_keys = d_keys or (d_model // n_heads) d_values = d_values or (d_model // n_heads) self.inner_correlation = correlation self.query_projection = nn.Linear(d_model, d_keys * n_heads) self.key_projection = nn.Linear(d_model, d_keys * n_heads) self.value_projection = nn.Linear(d_model, d_values * n_heads) self.out_projection = nn.Linear(d_values * n_heads, d_model) self.n_heads = n_heads def forward(self, queries, keys, values, attn_mask): B, L, _ = queries.shape _, S, _ = keys.shape H = self.n_heads queries = self.query_projection(queries).view(B, L, H, -1) keys = self.key_projection(keys).view(B, S, H, -1) values = self.value_projection(values).view(B, S, H, -1) out, attn = self.inner_correlation( queries, keys, values, attn_mask ) out = out.view(B, L, -1) return self.out_projection(out), attn class my_Layernorm(nn.Module): """ Special designed layernorm for the seasonal part """ def __init__(self, channels): super(my_Layernorm, self).__init__() self.layernorm = nn.LayerNorm(channels) def forward(self, x): x_hat = self.layernorm(x) bias = torch.mean(x_hat, dim=1).unsqueeze(1).repeat(1, x.shape[1], 1) return x_hat - bias class moving_avg(nn.Module): """ Moving average block to highlight the trend of time series """ def __init__(self, kernel_size, stride): super(moving_avg, self).__init__() self.kernel_size = kernel_size self.avg = nn.AvgPool1d(kernel_size=kernel_size, stride=stride, padding=0) def forward(self, x): # padding on the both ends of time series front = x[:, 0:1, :].repeat(1, (self.kernel_size - 1) // 2, 1) end = x[:, -1:, :].repeat(1, (self.kernel_size - 1) // 2, 1) x = torch.cat([front, x, end], dim=1) x = self.avg(x.permute(0, 2, 1)) x = x.permute(0, 2, 1) return x class series_decomp(nn.Module): """ Series decomposition block """ def __init__(self, kernel_size): super(series_decomp, self).__init__() self.moving_avg = moving_avg(kernel_size, stride=1) def forward(self, x): moving_mean = self.moving_avg(x) res = x - moving_mean return res, moving_mean class series_decomp_multi(nn.Module): """ Multiple Series decomposition block from FEDformer """ def __init__(self, kernel_size): super(series_decomp_multi, self).__init__() self.kernel_size = kernel_size self.series_decomp = [series_decomp(kernel) for kernel in kernel_size] def forward(self, x): moving_mean = [] res = [] for func in self.series_decomp: sea, moving_avg = func(x) moving_mean.append(moving_avg) res.append(sea) sea = sum(res) / len(res) moving_mean = sum(moving_mean) / len(moving_mean) return sea, moving_mean class EncoderLayer(nn.Module): """ Autoformer encoder layer with the progressive decomposition architecture """ def __init__(self, attention, d_model, d_ff=None, moving_avg=25, dropout=0.1, activation="relu"): super(EncoderLayer, self).__init__() d_ff = d_ff or 4 * d_model self.attention = attention self.conv1 = nn.Conv1d(in_channels=d_model, out_channels=d_ff, kernel_size=1, bias=False) self.conv2 = nn.Conv1d(in_channels=d_ff, out_channels=d_model, kernel_size=1, bias=False) self.decomp1 = series_decomp(moving_avg) self.decomp2 = series_decomp(moving_avg) self.dropout = nn.Dropout(dropout) self.activation = F.relu if activation == "relu" else F.gelu def forward(self, x, attn_mask=None): new_x, attn = self.attention( x, x, x, attn_mask=attn_mask ) x = x + self.dropout(new_x) x, _ = self.decomp1(x) y = x y = self.dropout(self.activation(self.conv1(y.transpose(-1, 1)))) y = self.dropout(self.conv2(y).transpose(-1, 1)) res, _ = self.decomp2(x + y) return res, attn class Encoder(nn.Module): """ Autoformer encoder """ def __init__(self, attn_layers, conv_layers=None, norm_layer=None): super(Encoder, self).__init__() self.attn_layers = nn.ModuleList(attn_layers) self.conv_layers = nn.ModuleList(conv_layers) if conv_layers is not None else None self.norm = norm_layer def forward(self, x, attn_mask=None): attns = [] if self.conv_layers is not None: for attn_layer, conv_layer in zip(self.attn_layers, self.conv_layers): x, attn = attn_layer(x, attn_mask=attn_mask) x = conv_layer(x) attns.append(attn) x, attn = self.attn_layers[-1](x) attns.append(attn) else: for attn_layer in self.attn_layers: x, attn = attn_layer(x, attn_mask=attn_mask) attns.append(attn) if self.norm is not None: x = self.norm(x) return x, attns class DecoderLayer(nn.Module): """ Autoformer decoder layer with the progressive decomposition architecture """ def __init__(self, self_attention, cross_attention, d_model, c_out, d_ff=None, moving_avg=25, dropout=0.1, activation="relu"): super(DecoderLayer, self).__init__() d_ff = d_ff or 4 * d_model self.self_attention = self_attention self.cross_attention = cross_attention self.conv1 = nn.Conv1d(in_channels=d_model, out_channels=d_ff, kernel_size=1, bias=False) self.conv2 = nn.Conv1d(in_channels=d_ff, out_channels=d_model, kernel_size=1, bias=False) self.decomp1 = series_decomp(moving_avg) self.decomp2 = series_decomp(moving_avg) self.decomp3 = series_decomp(moving_avg) self.dropout = nn.Dropout(dropout) self.projection = nn.Conv1d(in_channels=d_model, out_channels=c_out, kernel_size=3, stride=1, padding=1, padding_mode='circular', bias=False) self.activation = F.relu if activation == "relu" else F.gelu def forward(self, x, cross, x_mask=None, cross_mask=None): x = x + self.dropout(self.self_attention( x, x, x, attn_mask=x_mask )[0]) x, trend1 = self.decomp1(x) x = x + self.dropout(self.cross_attention( x, cross, cross, attn_mask=cross_mask )[0]) x, trend2 = self.decomp2(x) y = x y = self.dropout(self.activation(self.conv1(y.transpose(-1, 1)))) y = self.dropout(self.conv2(y).transpose(-1, 1)) x, trend3 = self.decomp3(x + y) residual_trend = trend1 + trend2 + trend3 residual_trend = self.projection(residual_trend.permute(0, 2, 1)).transpose(1, 2) return x, residual_trend class Decoder(nn.Module): """ Autoformer encoder """ def __init__(self, layers, norm_layer=None, projection=None): super(Decoder, self).__init__() self.layers = nn.ModuleList(layers) self.norm = norm_layer self.projection = projection def forward(self, x, cross, x_mask=None, cross_mask=None, trend=None): for layer in self.layers: x, residual_trend = layer(x, cross, x_mask=x_mask, cross_mask=cross_mask) trend = trend + residual_trend if self.norm is not None: x = self.norm(x) if self.projection is not None: x = self.projection(x) return x, trend class Autoformer(nn.Module): """ Autoformer is the first method to achieve the series-wise connection, with inherent O(LlogL) complexity Paper link: https://openreview.net/pdf?id=I55UqU-M11y """ def __init__(self, task_name='short_term_forecast',seq_len=96, label_len=48, pred_len=96, enc_in=7, dec_in=7, c_out=1, e_layers=2, d_layers=1, n_heads=8,factor=3, d_model=16, d_ff=32, des='Exp', expand=2, d_conv=4, top_k=5, embed='timeF',freq='h', dropout=0.1,num_kernels=6, moving_avg=25,channel_independence=1, decomp_method='moving_avg', use_norm=1, version='fourier', mode_select='random', modes=32, activation='gelu',seasonal_patterns='Monthly', inverse=False, mask_rate=0.25, anomaly_ratio=0.25,output_attention=False,down_sampling_layers=0, down_sampling_window=1, down_sampling_method=None, seg_len=48, num_workers=0, itr=1, train_epochs=100, batch_size=32, patience=3, learning_rate=0.0001, loss='MSE', lradj='type1', use_amp=False, use_gpu=True, gpu=0, use_multi_gpu=False, devices='0,1,2,3', p_hidden_dims=[128, 128], p_hidden_layers=2, use_dtw=False, augmentation_ratio=0, seed=2, jitter=False, scaling=False, permutation=False, randompermutation=False, magwarp=False, timewarp=False, windowslice=False, windowwarp=False, rotation=False, spawner=False, dtwwarp=False, shapedtwwarp=False, wdba=False, discdtw=False, discsdtw=False, extra_tag='', **kwargs): super(Autoformer, self).__init__() self.task_name = task_name self.seq_len = seq_len self.label_len = label_len self.pred_len = pred_len self.output_attention = output_attention # Decomp kernel_size = moving_avg self.decomp = series_decomp(kernel_size) # Embedding self.enc_embedding = DataEmbedding_wo_pos(enc_in, d_model, embed, freq, dropout) # Encoder self.encoder = Encoder( [ EncoderLayer( AutoCorrelationLayer( AutoCorrelation(False, factor, attention_dropout=dropout, output_attention=output_attention), d_model, n_heads), d_model, d_ff, moving_avg=moving_avg, dropout=dropout, activation=activation ) for l in range(e_layers) ], norm_layer=my_Layernorm(d_model) ) # Decoder if self.task_name == 'long_term_forecast' or self.task_name == 'short_term_forecast': self.dec_embedding = DataEmbedding_wo_pos(dec_in, d_model, embed, freq,dropout) self.decoder = Decoder( [ DecoderLayer( AutoCorrelationLayer( AutoCorrelation(True, factor, attention_dropout=dropout, output_attention=False), d_model, n_heads), AutoCorrelationLayer( AutoCorrelation(False, factor, attention_dropout=dropout, output_attention=False), d_model, n_heads), d_model, c_out, d_ff, moving_avg=moving_avg, dropout=dropout, activation=activation, ) for l in range(d_layers) ], norm_layer=my_Layernorm(d_model), projection=nn.Linear(d_model, c_out, bias=True) ) self.projection_final = nn.Linear(pred_len*enc_in, pred_len*c_out, bias=True) def forward(self, x_enc, x_mark_enc, x_dec, x_mark_dec): # decomp init mean = torch.mean(x_enc, dim=1).unsqueeze( 1).repeat(1, self.pred_len, 1) zeros = torch.zeros([x_dec.shape[0], self.pred_len, x_dec.shape[2]], device=x_enc.device) seasonal_init, trend_init = self.decomp(x_enc) # decoder input if self.label_len == 0: trend_init = trend_init seasonal_init = seasonal_init else: trend_init = torch.cat([trend_init[:, -self.label_len:, :], mean], dim=1) seasonal_init = torch.cat([seasonal_init[:, -self.label_len:, :], zeros], dim=1) # enc enc_out = self.enc_embedding(x_enc, x_mark_enc) enc_out, attns = self.encoder(enc_out, attn_mask=None) # dec dec_out = self.dec_embedding(seasonal_init, x_mark_dec) seasonal_part, trend_part = self.decoder(dec_out, enc_out, x_mask=None, cross_mask=None,trend=trend_init) # final dec_out = trend_part + seasonal_part dec_out=dec_out[:, -self.pred_len:, :] dec_out=self.projection_final(dec_out.view(dec_out.shape[0], -1)) return dec_out from pytorch_forecasting.models import BaseModel from typing import Dict class AutoFormerNetModel(BaseModel): def __init__(self,seq_len=24, label_len=0, pred_len=1, enc_in=7, dec_in=7, c_out=1, e_layers=2, d_layers=1, factor=3, d_model=16, d_ff=32, des='Exp', itr=1, top_k=5,embed='timeF',freq='h', dropout=0.1,num_kernels=6, **kwargs): # saves arguments in signature to `.hparams` attribute, mandatory call - do not skip this self.save_hyperparameters() # pass additional arguments to BaseModel.__init__, mandatory call - do not skip this super().__init__(**kwargs) self.network = Autoformer( seq_len=seq_len, label_len=label_len, pred_len=pred_len, enc_in=enc_in, dec_in=dec_in, c_out=c_out, e_layers=e_layers, d_layers=d_layers, factor=factor, d_model=d_model, d_ff=d_ff, des=des, itr=itr, top_k=top_k, embed=embed, freq=freq, dropout=dropout, num_kernels=num_kernels ) self.label_len=label_len # 修改,锂电池预测 def forward(self, x: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]: x_enc = x["encoder_cont"][:,:,:-1] # torch.Size([100, 10, 9]) x_dec = torch.cat([x["encoder_cont"][:, -self.label_len:, :-1], x["decoder_cont"][:,:,:-1]], dim=1) # torch.Size([100, 11, 9]) # 输出 prediction = self.network(x_enc=x_enc,x_mark_enc=None,x_dec=x_dec,x_mark_dec=None) # 输出rescale, rescale predictions into target space prediction = self.transform_output(prediction, target_scale=x["target_scale"]) # 返回一个字典,包含输出结果(prediction) return self.to_network_output(prediction=prediction) if __name__=='__main__': N,L,C=100,96,15 label_len = 16 c_out = 1 pred_len=16 x_enc=torch.ones((N,L,C)) x_mark_enc=torch.ones((N, L, 4)) x_dec = torch.ones((N, pred_len, C)) x_mark_dec=torch.ones((N, pred_len, 4)) model=Autoformer(seq_len=L, enc_in=C, dec_in=C, label_len = label_len, pred_len=pred_len, c_out=1) # pred_len 被限制了 out=model(x_enc=x_enc, x_mark_enc=x_mark_enc, x_dec=x_dec, x_mark_dec=x_mark_dec) print(out.shape)